Piezoelectric transducers for a variety of applications, including hydrophones, are well known. Piezoelectric devices respond to an application of stress, such as externally applied pressure, to develop an electrical potential. Conversely, piezoelectric devices develop a mechanical response with a voltage is applied. The behavior and characteristics of piezoelectric materials is well described in IEEE Standard on Piezoelectricity, 1978, incorporated herein by reference.
The earliest such applications for transducers were entirely analog. With the advent of digital technology, however, digital techniques were soon applied to signal detection and processing. This digital technology, in general, is capable of higher resolution than the previous analog techniques.
The earliest digital signal acquisition and processing data rates were extremely slow, and had fewer bits per sample, compared with the state of the art today. With slow bit rates, distortion produced by the piezoelectric crystals was relatively insignificant. In this context, the term "distortion" refers to the increasing significance of harmonics, particularly the second harmonic, compared to the fundamental of the signal, with increasing signal output. In other words, as stress on the piezoelectric device, for example in the form of pressure, increases, the amplitudes of the harmonics produced by the crystal increase at a rate that is faster than the rate of increase in the amplitude of the fundamental. However, as digital signal processing has increased in speed and resolution, the distortion of the signal from the harmonics has become more and more important. The clarity and resolution is thus dependent more and more on the signal from the transducer being relatively undistorted.
In real seismic applications, noise from the background and other sources is of much higher amplitude than the return signal of interest. A variety of techniques, such as correlation, have been developed to extract the reflected, desired signal from this background noise. The non-linearity in the signal from the crystal will cause inter-modulation between the background noise and the desired signal. In other words, the desired signal will be amplitude modulated by the much larger noise signal, generating new families of modulation products, complicating the filtering process.
Equipment improvements in data rate, resolution, and linearity bring better definition in resultant profiles, to the point that errors and distortion from the transducer contribute most of the signal error. That means that an improvement in the accuracy of the transducer brings an immediate improvement in signal quality.
A further difficulty lies in the fact that, since there is no perfect transducer, there is no standard against which to measure the distortion from a transducer. This is illustrated in FIG. 10, page 36, in the previously mentioned IEEE Standard on Piezoelectricity.
Thus, there remains a need for a method and system to eliminate or at least minimize the effects of signal distortion from the active element in a transducer, such as a piezoelectric device. Such a method and system should eliminate the distortion effects of the piezoelectric device, despite the non-linearity of the element itself. The system should be self-contained and not have to rely on any other signal processing steps or other active elements such as transistors.